Try paint stripper. It will not harm the wood, but do not allow to get on floor or other areas. I use "Dad's Easy Stripper". Make sure you follow instructions on can. My 76 Sov is doing the same thing in areas. I plan to pull paper off and paint. As far as the endcaps go, mine appear to be fine so I don't know what to say there.
Actually before I used paint stripper, you should try Laquer Thinner, or MEK. If either works, you'll notice immediately because the glue will gum-up. You can then take a plastic putty knife to scrape the gummey glue off without cutting into the wood.